Movement through space or movement through time?

A particle that moves a certain distance in the gravitational field of
a small mass,changes its weight as it moves.But if that particle had
been stationary relative to the small mass, and the gravitational
field had
changed its strength with time, in such a way that the weight of the
stationary particle, from one moment to the next, was exactly the same
as the weight of the moving particle from one moment to the next,a
clock close to the particle at all instants of time, would measure
the same time elapsed in both cases.If I looked at the time on the
clock, I wouldn't know if the particle had been moving or
stationary.If the electric field and other fields behaved in this
manner, would I be able to distinguish between a movement
through space in the presence of non-oscillating fields and a
movement through time in the presence of oscillating fields?

The ideas are fundamental, the language is primary. Particals and clocks, weight instead of mass, no mention of field or symmetry. How can we talk with words that have not been carefully defined?

The short answer is that movement, that is change, requires description involving some of at least three spatial and one time dimension. No movement can take place in space devoid of time, and if there were only time, no space, where would change take place? So we must speak of change in terms that involve both space and time, at least one dimension of space and one dimension of time, like a string that is only vibrateing by compression waves along its own lenth, and not in any secondary lateral sense.

Of course no real string vibrates in such a limited fashion. But for the sake of greater understanding we may refer to such a linear motion, given the existance of one dimension in time and one in space. We can even draw pictures of such an idea, altho most images we commonly look at are of two spatial dimensions, with variations in color and texture to suggest real objects, like buildings and trees. And if we choose three dimensions in space and one in time we can talk about complicated motions like orbits and objects in free-fall and what it is we mean by a frame of reference, and all of this is already described by great minds who have given us much understanding with beauty and elegance.

When you are making descriptions, you get to choose which dimensions and which operations you intend to describe. It is a sort of game which has its own rules that have been laid down in history, and we need to learn those rules in order to play, that is to talk to each other, about what is going on with weight and motion of various kinds. It seems you are kurious, but how far curiosity takes you is up to you.